For if Pittsburgh general manager Ray Shero — perhaps under orders from team chairman Mario Lemieux — dismisses coach Dan Bylsma in the wake of his club’s sweep by the Bruins in the Eastern Conference finals that was cemented in Boston last night with a 1-0 Game 4 loss, the 2009 Stanley Cup-winner would immediately vault to the top of the list of candidates for the vacancy behind the Blueshirts’ bench.

That is, if Shero were to grant Rangers GM Glen Sather permission to speak to Bylsma, who is under contract to the Penguins through the end of next season.

The Rangers are expected to at least initially address the club’s coaching search at their organizational meetings at Sather’s Western White House in La Quinta, Calif., which will commence Monday.

It is unknown whether Sather will conduct formal interviews with candidates during the week, though it would seem an appropriate time.

The Blueshirts have received permission to speak with former Vancouver coach Alain Vigneault, fired by the Canucks after a second consecutive first-round playoff exit following a Game 7 defeat in the 2011 Finals, and AHL Toronto Marlies’ coach Dallas Eakins. They are expected to ask for permission to speak with Lindy Ruff, dismissed in February by the Sabres after 14-plus seasons in Buffalo.

Dave Tippett, who remains under contract to the Coyotes through June 30, has made it clear his first preference is to remain in Phoenix if ownership issues can be resolved. Mark Messier remains in the picture, though it is unclear whether Sather is willing to even entertain the notion of taking the leap of faith that would be required in order to hire an individual absent of any coaching experience.